An ohmic device exhibits the following relationship between resistance, voltage, and current:
R = V / I
(This is Ohm's Law.) This means that the resistance of an ohmic device is independent of the voltage applied across it. If a graph of voltage vs. current was plotted for a specific ohmic device, the graph would be a straight line, and the slope of this line would be the device's resistance. Note, however, that current vs. voltage graphs (or "I-V diagrams") are more common; in which case the resistance is the inverse of the slope.
In reality, there cannot be truly ohmic devices, such as ideal resistors. Common non-ohmic devices are light bulbs and diodes.